Finite Group Databasebeta

?

← Prev (#7635887) Next (#7635889) →

C₂×#38732 #7635888

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

7016 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 26 points:

(1,2);(3,4)(5,9)(6,7)(8,10)(11,12,16,15)(13,18,14,17);(4,7)(8,9)(12,15)(17,18)(20,23)(24,26);(11,13,16,14)(12,17,15,18)(19,20)(21,24)(22,23)(25,26);(3,5,6,10)(4,8,7,9)(11,14,16,13)(12,18,15,17)(19,21,22,25)(20,24,23,26);(3,4)(5,8)(6,7)(9,10)(11,15,16,12)(13,18,14,17)(19,20)(21,24)(22,23)(25,26)

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7543084);